Question: The equation of a circle $C$ is $x^2+y^2-10x+16y+64 = 0$. What is its center $(h, k)$ and its radius $r$ ?
To find the equation in standard form, complete the square. $(x^2-10x) + (y^2+16y) = -64$ $(x^2-10x+25) + (y^2+16y+64) = -64 + 25 + 64$ $(x-5)^{2} + (y+8)^{2} = 25 = 5^2$ Thus, $(h, k) = (5, -8)$ and $r = 5$.